The present invention relates to boundary surface measurement for detecting the shape of the wall of a deep hole or groove provided in the surface of, for example, a silicon wafer, and for detecting the shape of, for example, an air bubble or foreign particle contained in a cell of a living being.
As the integration density of a semiconductor device has been greatly increased in recent years, a semiconductor device is changing from a two-dimensional structure to a three-dimensional structure. Accordingly, in order to electrically insulating adjacent elements of the semiconductor device from each other, it has been put to practical use to provide a deep groove between adjacent elements. Further, in order to obtain a large electric capacitance in a small area, it has been tried to provide a deep hole having a small aperture in a semiconductor substrate. However, the characteristics of semiconductor elements are greatly affected by the shape of the groove or hole (hereinafter generically referred to as "hole"), and hence each semiconductor element is required to have a hole of the same shape. Accordingly, it is neccessary to check the shape of the hole, and hence means for measuring the shape of the hole is earnestly desired. However, it is impossible to find an apparatus capable of observing a deep hole provided in the surface of a silicon wafer. The term "deep hole" used herein indicates, for example, a hole having an aperture diameter of 1 .mu.m and a depth of 10 .mu.m (namely, a hole having a relative depth of 10 .mu.m.div.1 .mu.m+10). According to a prior art, only a shallow hole provided in the surface of a body or the gentle unevenness of the above surface can be measured. For example, a shallow hole having an aperture diameter of 10 .mu.m and a depth of 1 .mu.m (namely, a hole having a relative depth of 1 .mu.m.div.10 .mu.m=0.1) can be readily measured. Accordingly, a hole having an aperture diameter of 100 .mu.m and a depth of 10 .mu.m can also be measured. However, in a case where the cross section of a hole has a rectangular shape or circular shape, that is, the hole has a wall perpendicular to the surface or a circular wall, it is impossible to measure such a hole by the prior art.
A hole having an infinitesimal aperture can be thought as a special example of a deep hole. When the aperture diameter of a deep hole is made equal to zero, the deep hole becomes a void. Observation of voids will be frequently required in a process for fabricating a semiconductor device having a three-dimensional structure, and is also necessary for detecting and measuring the shape of an air bubble or foreign particle contained in a cell of a living being, in the field of biotechnology. However, the observation and measurement of a void in silicon cannot be made by any conventional apparatus, as a deep hole in the surface of silicon cannot be measured.
As mentioned above, the prior art cannot satisfy recent requirements with respect to surface measurement. Now, widely-used, conventional methods of measuring the surface of a body (that is, one mechanical method and three optical methods) will be explained below in detail, to clarify the drawbacks of the prior art.
FIG. 3 shows the fundamental construction of an apparatus for mechanically measuring the unevenness of a surface. Referring to FIG. 3, a stylus 1 is kept in contact with a body 2 which is to be measured, under a predetermined pressure, to measure the unevenness of the surface of the to-be-measured body 2 mounted on a sample holding table 4 which can move on a base stage 3. The stylus 1 is connected with a plunger 5 of a displacement detector (for example, a differential transformer) 6. When the stylus 1 rises and falls, the amount of displacement is indicated on a meter 7 through the detector 6. When the sample holding table 4 is moved in a direction indicated with an arrow 8, the to-be-measured body (hereinafter referred to as "sample") 2 moves together with the table 4, and hence the stylus 1 rises and falls in accordance with the surface state of the sample 2. A relation between the movement of the stylus 1 in a vertical relation and the movement of the sample 2 in a horizontal direction can be determined, and hence the unevenness of the surface concerned can be determined. Often the unevenness must be determined with accuracies as high as several nanometers. However, the tip of the stylus 1 has a radius of 1 .mu.m or more, and hence the stylus 1, as shown in FIG. 4A, cannot be inserted in a deep hole 2a which is provided in the surface of the sample 2 and has an aperture diameter of 1 .mu.m. That is, the shape and depth of the hole 2a cannot be measured by the stylus 1. Further, in the above-mentioned apparatus for mechanically measuring the unevenness of surface, the sample 2 is moved while being kept in contact with the stylus 1, and hence the sample surface may be damaged. The above mechanical measurement is a sort of destructive inspection, and has not been recommended in recent years.
Accordingly, attention has been paid to optical methods capable of performing non-destructive inspection. Of many optical means for observing and measuring the state of a surface (including the unevenness of a surface), an optical microscope is most widely used. Various optical microscopes have been known which are different in function from each other. Now, the measurement of surface unevenness made by reflection optical microscopes (a typical one of which is a metallurgical microscope) will be explained below, by way of example. In general, the optical microscopes are used for observing a fine structure on a flat surface, and cannot detect the exact structure of an uneven surface, since the unevenness of the surface often exceeds the focal depth of the optical microscope. Specifically, in a case where the magnification of an optical microscope is large, the vertical movement of a sample in a range from 1 to 10 .mu.m will cause a large amount of defocus of an observed point on the sample. By utilizing this phenomenon, the unevenness of surface can be observed by the optical microscopes. In more detail, the objective lens of the optical microscope is moved in relation to a sample so as to visually detect that the focal point is placed on the surface of the sample, and the unevenness of the surface can be determined on the basis of the variation in position of focal point with the horizontal movement of the sample. However, it is impossible to obtain the reflected light from the bottom of a deep hole, and hence the deep hole is observed only as a black spot. Accordingly, the above-mentioned method is unapplicable to the measurement of a deep hole which is the subject of the present invention.
The above method can be used for measuring the depth of a shallow hole, since the reflected light from the bottom of the shallow hole can reach an optical microscope. In this case, however, the accuracy of depth measurement is not good for the following reason. The position of the focal point is judged on the basis of the contrast of the image observed visually by an operator. In an ordinary optical microscope, reflected light from a defocussed portion is also received by the operator's eyes through the optical microscope, and thus acts as the background light. The contrast of the image of an observed surface portion which is coincident with a focal plane, is lowered by the above background light, and hence it is difficult to determine the focal plane. That is, it is impossible to determine the focal plane with accuracies of 1 .mu.m or less. Accordingly, the above method (that is, a first optical method) is inferior in accuracy of measurement to the mechanical method. The accuracy of measurement can be increased by making the field of view infinitesimal (that is, by placing a pinhole at the focal point of the eyepiece). In this case, however, the optical microscope does not function as the microscope, but becomes an optical, surface measuring apparatus which will be mentioned below.
As mentioned above, a conventional deflection optical microscope can measure only the depth of a shallow hole with accuracies of several micrometers. The unevenness of a surface having a shallow hole can be very accurately measured by using the interference between light rays reflected from the surface. This method is the second optical method for measuring the surface of a sample, and is widely used for measuring the thickness of a film. Although the principle of this method is well known to the art, brief explanation thereof will be made, with reference to FIG. 5. Referring to FIG. 5, when coherent light rays 9a and 9b are incident on the surface of the sample 2', light rays 10a and 10 b are reflected from the surface. The phase of the light ray 10a is different from that of the light ray 10b by an amount corresponding to an optical path difference which results from the step at the surface. Thus, an interference pattern is formed on an appropriate plane 11. The step and the unevenness of the surface of the sample 2' can be quantitatively determined by analyzing the interference pattern.
A main feature of this interference method is to measure the unevenness of a surface very accurately, and the unevenness in a range from 1 to 10 nanometers can be readily measured by this method. However, the interference method cannot be applied to a deep hole. Referring to FIG. 4B, when a light ray 9b' is incident on the wall of the deep hole 2a, a reflected light ray 10b' from the wall travels toward a bottom portion of the hole 2a, and hence cannot be observed at a place above the hole 2a. Thus, only an aperture diffraction pattern is observed. It is needless to say that the aperture diffraction pattern does not have information on the depth of the hole 2a but has only information on the aperture diameter of the hole 2a.
The first and second optical methods are lowest and highest in accuracy of measurement, respectively. Next, explanation will be made of a third optical method having an intermediate accuracy of measurement. This method is described in an article entitled "Optical Profilometer for Monitoring Surface Contours of Si Power Devices" (SPIE, Vol. 398, 1983, pages 266 to 275). An apparatus for carrying out the third optical method will hereinafter be referred to as an optical, surface measuring apparatus. FIG. 6A shows the fundamental construction of this apparatus. Referring to FIG. 6A, a sample 2 is placed on a sample holding table 21 which can move not only in a horizontal direction but also in a vertical direction, and the table 21 is placed on a base stage 22. A light beam 13 emitted from a light source 12 passes through a half-mirror 15, and is then focussed by a lens 16 so that a focal point 13' is formed on the surface of the sample 2. An essential feature of the apparatus of FIG. 6A resides in that the light beam 13 has a relatively short wavelength. As a result, a large amount of reflected light is generated at the focal point 13'. The reflected light passes through the lens 16, and is then reflected from the half-mirror 15 so as to form a light beam 14. The light beam 14 is focussed on a focal point 14' by a lens 17, and thus a small light spot is formed at the focal point 14'. The light beam 14 which has been focussed as mentioned above, passes through a pinhole provided in a pinhole plate 18, and is then received by a photodetector 19. The quantity of light incident upon the photodetector 19 is indicated by a meter 20.
As is well known, the optical system shown in FIG. 6A is a confocal system, and hence the image of a point deviating from the focal point 13' is formed at a position deviating from the focal point 14'. When the surface of the sample 2 is spaced apart from the focal point 13' by moving the sample holding table 21 in the vertical direction, a large light spot is formed on the surface of the sample 2, and hence the light spot at the focal point 14' becomes large. Thus, the quantity of light capable of passing through the pinhole and reaching the photodetector 19 is decreased. Further, when the sample 2 is brought near to the lens 16, the light spot on the surface of the sample 2 becomes large, and hence the diameter of the light spot on the pinhole plate 18 is increased. As a result, the light quantity indicated by the meter 20 decreases.
The above fact can be shown by a curve 23 of FIG. 6B. In FIG. 6B, the position of the sample holding table 21 in the vertical direction is plotted as abscissa, and the light quantity received by the photodetector 19 as ordinate. Further, reference symbol Z.sub.o designates that position of the sample holding table 21 where the focal point 13' is placed on the surface of the sample 2. Referring to FIG. 6B, when the focal point 13' deviates from the surface of the sample 2 in an upward or downward direction, the light quantity received by the photodetector 19 decreases.
As can be seen from FIG. 6B, the position Z.sub.o of the table 21 where the light quantity received by the photodetector 19 becomes maximum, can be determined by moving the table 21 which is mounted with the sample 2, in the vertical direction after the table 21 and the sample 2 have been displaced in the horizontal direction by a predetermined amount. In many cases, in order to accurately determine the position Z.sub.o, a curve 24 shown in FIG. 6C is used in place of the curve 23. The curve 24 is obtained by differentiating the curve 23, and a position where the differentiated light quantity curve, namely, the curve 24 takes a value 0, indicates the position Z.sub.o. The optical, surface measuring apparatus of FIG. 6A can measure the unevenness of a sample surface in the above-mentioned manner. Accuracy, with which the above apparatus can measure the unevenness of surface, is intermediate between the accuracy of the first optical method using an optical microscope and the accuracy of the second optical method utilizing the interference between reflected light rays. In many cases, accuracy of about 0.1 .mu.m is obtained by the optical, surface measuring device of FIG. 6A. Moreover, this apparatus can measure the unevenness of surface in a non-destructive manner, and hence is superior in practicability to other conventional apparatuses.
However, in order for the apparatus of FIG. 6A to have the above accuracy, it is required to make small the focal depth at the focal point 13'. Accordingly, the lens 16 is required to have a large aperture and a short focal length. As a result, the converging angle at the focal point 13' becomes large. Accordingly, when the apparatus of FIG. 6A is used for measuring the deep hole 2a, a surface area surrounding the deep hole 2a, as shown in FIG. 4C, prevents the focal point 13' from being formed in the hole 2a. In other words, the apparatus of FIG. 6A is unapplicable to the measurement of a deep hole.
Next, explanation will be made on the limit of the performance of the apparatus of FIG. 6A. In this apparatus, as shown in FIG. 6C, the position Z.sub.o where the focal point 13' is placed on the surface of the sample 2, is given by a position where the variation of received light quantity with the vertical displacement of the sample is zero. However, it is very difficult to detect a position where the differentiated value of received light quantity is exactly equal to zero, by using an electric circuit. Usually, a voltage signal within a range from +.DELTA.V/2 to -.DELTA.V/2 (or a current signal corresponding thereto) is detected for the position Z.sub.o. The above recognition width .DELTA.V is generally called a "window" width. Taking into consideration the noise level of a signal amplifier, the "window" width is set to a finite value. The "window" width will be explained below in more detail, with reference to FIG. 7A. In FIG. 7A, a differentiated light quantity curve 24' is the same as the curve 24 of FIG. 6C. It can be seen from FIG. 7A that owing to the "window" width, the position Z.sub.o is determined within a range .DELTA.Z. Not only the noise level of the signal amplifier but also the zero-drift thereof make the "window" width large. The zero-drift, that is, the variation of the zero level of the signal amplifier is caused by variations in room temperature and others. The noise and zero-drift of the signal amplifier are both unavoidable. Referring now to FIG. 7A, when a zero-drift voltage .DELTA.Vd is generated, the differentiated light quantity curve 24' is moved to a broken curve 24a. Thus, the position Z.sub.o is seemingly moved to a point Z.sub.o . Thus, a gross error will be produced in determining the position Z.sub.o. Accordingly, in the conventional method using differentiated light quantity, the accuracy .DELTA.Z.sub.o of measurement is as low as .+-.0.1 .mu.m.
As can be seen from FIG. 7A, the accuracy .DELTA.Z can be improved by making steep the slope of the curve 24'. This corresponds to an increase in the detected light quantity shown in FIG. 6B. However, the detected light quantity can be increased only in a limited range, and thus the accuracy .DELTA.Z, as mentioned above, is as low as .+-.0.1 .mu.m. On the other hand, when the detected light quantity is decreased, a state such as shown in FIG. 7B occurs. Referring to FIG. 7B, the slope of a differentiated light quantity curve 24b is gentle, and thus the accuracy, with which the position Z.sub.o is determined, is changed from .DELTA.Z to .DELTA.Z' for the same "window" width, that is, is greatly reduced. The above reduction in accuracy due to a decrease in light quantity is a fatal drawback of the optical, surface measuring apparatus of FIG. 6A. In a case where the wavelength of the light beam 13 is such that the sample 2 transmits the light beam 13, the above drawback becomes remarkable. That is, the reflected light from the sample 2 is greatly decreased, and hence the state of FIG. 7B occurs. Thus, the unevenness of surface cannot be measured from the practical point of view. Accordingly, it is impossible to measure a material which produces only a small amount of reflected light, by the optical, surface measuring apparatus of FIG. 6A.
As mentioned above, the conventional apparatus of FIG. 6A has three drawbacks mentioned below.
(1) The apparatus is unapplicable to a material generating only a small amount of reflected light (that is, a material capable of transmitting the light beam 13).
(2) The accuracy of measurement is dependent upon the detected light quantity.
(3) The "window" width in detecting a zero point cannot be made very small, because of variations in zero level of an electric circuit, and hence it is impossible to greatly improve the accuracy of measurement.
The fact that the apparatus of FIG. 6A is unapplicable to the measurement of deep hole, is related to the first one of the above drawbacks. Further, it is to be noted that the first, second and third drawbacks mentioned above are all caused by the fact that the position Z.sub.o is determined using differentiated light quantity.